If you need a background image, you can use CircleAvatar with IconButton. Set the backgroundImage property.
CircleAvatar(
backgroundImage: NetworkImage(userAvatarUrl),
)
Example with button:
CircleAvatar(
backgroundColor: Colors.blue,
radius: 20,
child: IconButton(
padding: EdgeInsets.zero,
icon: Icon(Icons.add),
color: Colors.white,
onPressed: () {},
),
),